The FZ53 camera does come with 8MB of internal memory, but this is just enough to take a couple of photos to test/check the camera. You will need to purchase a standard SD Card (separately).
Make sure the standard SD card is Class 4 or higher and no more than 32GB of storage space. Using a card with more than that (64GB, 12GB, etc.) will not work and is not recommended.
You can also save money and just buy a standard "SD" or "SDHC" card. Do not use an "Ultra", "SDXC" or "High Speed" card as these are not necessary and are not recommended.